States would get the grants if their legislation met certain criteria, primarily that family members or a law enforcement officer can petition for an individual's gun to be taken away if that person poses a threat to themselves or others. The law must require due process protections before an order can be issued, such as proper notice and a formal hearing. And states must establish a minimum penalty if a person files false allegations against an individual.

The federal proposal comes after it was discovered that gunman Nikolas Cruz had exhibited several warning signs before he massacred 17 people at a high school in Parkland, Florida, three weeks ago. Rubio said it's unclear whether this bill would have prevented the shooting, but that it would have been a tool for those who did have concerns about Cruz.

"This certainly would have provided an option that today does not exist," Rubio said at a news conference Wednesday. "If today you believe someone was going to do something like this, you can report it, but there's very little you can do to remove guns from someone until that person's adjudicated, gone to jail or something like that."

Nelson, standing next to Rubio, said he still wants to see more legislation from Congress -- such as universal background checks -- but argued their bill "is a good step in the right direction."

Gun violence restraining orders are currently in place in five states: California, Connecticut, Indiana, Oregon and Washington. Even before the Parkland shooting, similar proposals were being considered by at least 19 state legislatures.

Whether such a proposal could pass Congress remains unclear, as even some of the narrowest proposals for increased gun control have stalled out in the US legislative branch. The Senate formally moved on to considering a banking bill after legislation to incentivize states to improve reporting to the national criminal background check database appeared unable to win 60 votes. Legislators have said they're still negotiating and searching for a viable solution on that and other proposals.

Rubio said "a number" of his colleagues have expressed openness to the bill and he's been working with staffers of Sen. Chuck Grassley, the Iowa Republican who chairs the Senate Judiciary Committee, and he's hoping to "get him on board."

The House of Representatives is set to vote on a bill next week that will give schools more money to strengthen security. Pressed on why Congress has not voted on any other gun-related bills since the Parkland shooting, Rubio argued that Congress, by nature, doesn't move as quickly as state legislatures.

Rubio -- who, along with Nelson, has been in the spotlight on gun issues since attending a CNN town hall last month -- argued Congress needs to focus on bills that have more bipartisan support before it moves on to controversial legislation like raising the age requirement to buy a rifle or a ban on assault-style weapons.

"I just think where we find common ground, we need to begin the work and get things done, because this is not taxes or some other issue," he said. "Even as I speak to you now, the next killer like this could be out there plotting their move."

Rubio said he has not spoken to the National Rifle Association about this bill but defended potential criticism that it could violate an individual's right to bear arms.

"Every constitutional right we have could potentially -- through a court order -- be infringed upon. They can go into your property with a subpoena or with a search warrant. They can get your records through a subpoena," he said. "So that's why the due process at the front end is important. There has to be a standard that has to be met. And this clearly creates the ability for states, or incentivizes states, to do so."

A spokesperson told CNN the NRA will not comment until the full text of the bill is published.

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